1. Field of the Invention
The present invention relates to a method and apparatus for measuring the concentration of a component of a gas to be measured (hereinafter referred to as a xe2x80x9cgas under measurementxe2x80x9d). In particular, the invention relates to measuring the concentration of nitrogen oxides (hereinafter referred to as xe2x80x9cNOxxe2x80x9d) in a gas under measurement. More particularly, the invention relates to a method for measuring the concentration of NOx in exhaust gas from, for example, a combustor or an internal combustion engine.
2. Description of the Prior Art
Conventionally, a method for measuring the concentration of NOx in a gas under measurement employs an NOx concentration sensor including a first chamber and a second chamber, each including an oxygen ion pump cell.
According to the conventional method, first, a gas under measurement (for example, exhaust gas from a combustor or an internal combustion engine) is introduced into the first chamber through a first diffusion passage (for example, a diffusion controlling hole). A pump voltage is applied to a first oxygen ion pump cell of the first chamber in order to pump out oxygen from the first chamber such that oxygen concentration measured at an inlet to the second chamber becomes constant and such that the voltage of an oxygen-concentration-measuring cell becomes constant. At this time, not only is oxygen contained in the introduced gas decomposed, but also nitrogen monoxide contained in the gas is decomposed to a certain extent. The first pump current Ip1 flowing to the first oxygen ion pump cell is measured. The first pump current Ip1 is proportional to the amount of oxygen ions generated through decomposition of oxygen and nitrogen monoxide contained in the gas introduced into the first chamber.
Next, the gas under measurement contained in the first chamber is introduced into the second chamber through a second diffusion passage (for example, a diffusion controlling hole). A pump voltage is applied to a second oxygen ion pump cell of the second chamber so as to decompose nitrogen monoxide contained in the introduced gas and to pump out oxygen from the second chamber. The second pump current Ip2 flowing through the second oxygen ion pump is measured.
FIG. 3 shows the relationship between the concentration of NOx in the gas under measurement introduced into the first chamber and the second pump current Ip2. From the relationship shown in FIG. 3, the concentration of NOx is obtained by expression (1).
NOx concentration=G(I2xe2x88x92xcex2)xe2x80x83xe2x80x83(1) 
where
xcex2: Offset component of second pump current Ip2 
G: Gain ppm/A
The offset component xcex2 is the value of the second pump current Ip2 as measured at an NOx concentration of 0 ppm and corresponds to a pump current which is generated in relation to decomposition of residual oxygen which has not been decomposed in the first chamber and remains in the gas introduced into the second chamber.
Measurement of the offset component xcex2 employs a standard gas having an NOx concentration of 0 ppm and a known oxygen concentration. The offset component xcex2 is measured through measurement of the second pump current Ip2 while the concentration of oxygen in the standard gas is varied. Measurement of the gain G employs a standard gas having a constant oxygen concentration and a known NOx concentration. The gain G is measured through measurement of the second pump current Ip2 while the concentration of NOx in the standard gas is varied. The gain G and the offset component xcex2 depend on the concentration of oxygen in the gas under measurement, whereas the concentration of oxygen in the gas under measurement is measured substantially accurately through measurement of the first pump current Ip1. Accordingly, the gain G must be corrected on the basis of the first pump current Ip1.
However, according to the above-described method, the NOx concentration can be measured accurately in a measurement region in which the second pump current Ip2 has a high value (a measurement region in which NOx concentration is high), whereas the NOx concentration cannot be measured accurately in a measurement region in which the second pump current Ip2 has a low value.
It is confirmed that the first pump current Ip1 is proportional to the concentration of oxygen in the gas under measurement. However, the reason why the above-mentioned expression (1) does not hold in the measurement region in which NOx concentration is low cannot be satisfactorily explained from a physical phenomenon associated with diffusion.
An object of the present invention is to solve the above-mentioned problems, and to provide a method for accurately measuring the concentration of NOx in a gas under measurement even in a measurement region in which NOx concentration is low.
To achieve the above object, the present invention provides a method for measuring the concentration of NOx in a gas under measurement by use of an NOx concentration sensor comprising: a first chamber equipped with a first oxygen ion pump cell, which comprises a solid electrolyte layer and a pair of electrodes; a second chamber equipped with a second oxygen ion pump cell, which comprises a solid electrolyte layer and a pair of electrodes; a first diffusion passage for establishing communication between the first chamber and the gas under measurement; and a second diffusion passage for establishing communication between the first chamber and the second chamber. The method comprises the steps of: applying a pump voltage to the first oxygen ion pump cell so as to reduce the concentration of oxygen in the gas under measurement to be introduced into the second chamber to such an extent that nitrogen monoxide is decomposed within the first chamber, as well as to pump out oxygen generated through decomposition of nitrogen monoxide, or pump oxygen into the first chamber; applying a pump voltage to the second oxygen ion pump cell in order to decompose nitrogen monoxide contained in the gas under measurement introduced into the second chamber; measuring a first pump current flowing through the first oxygen ion pump cell; measuring a second pump current flowing through the second oxygen ion pump cell; and obtaining from the second pump current the concentration of NOx in the gas under measurement introduced into the first chamber by use of a nonlinear expression which expresses an approximated relationship between the second pump current and the concentration of NOx in the gas under measurement.
Since, according to the present invention, the NOx concentration is determined by use of a nonlinear expression which expresses an approximated relationship between the second pump current and the concentration of NOx in the gas under measurement, the NOx concentration can be determined more accurately even in a measurement region in which NOx concentration is low, as compared to the conventional method that employs a linear expression.
Preferably, in the method for measuring the concentration of NOx in a gas under measurement, the concentration of oxygen in the gas under measurement introduced into the first chamber may be obtained from the first pump current by use of a nonlinear expression which expresses an approximated relationship between the first pump current and the concentration of oxygen in the gas under measurement.
Preferably, in the method for measuring the concentration of NOx in a gas under measurement, a coefficient of the nonlinear expression may be obtained from the first pump current.
Preferably, in the method for measuring the concentration of NOx in a gas under measurement, a provisional NOx concentration may be obtained from the second pump current by use of a linear expression which approximates the NOx concentration in terms of the second pump current, and the thus obtained provisional NOx concentration may be corrected by use of an expression of higher order to thereby obtain the concentration of NOx in the gas under measurement introduced into the first chamber. Notably, a coefficient of the expression of higher order is obtained from the relationship between the provisional NOx concentration and an actual NOx concentration.
Preferably, in the method for measuring the concentration of NOx in a gas under measurement, a provisional NOx concentration may be obtained from the second pump current by use of a linear expression which approximates the NOx concentration in terms of the second pump current, and a deviation of the provisional NOx concentration from an actual NOx concentration as approximated by an expression of higher order may be added to the provisional NOx concentration to thereby obtain the concentration of NOx in the gas under measurement introduced into the first chamber.
Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings.